Computational Complexity and other fun stuff in math and computer science from Lance Fortnow and Bill Gasarch

Thursday, May 05, 2011

How has the STRUCTURES, OH- I mean CCC Conference changed: Lets look at the Call For Papers

Complexity theory has changed over the years.
How to really track these things?
One way is to look at the list of topics on the Call For papers for the
CCC conference (called STRUCTURES until the name changed, another sign of change).
Below I include pointers to the call for papers from
1986, 1997, and 2008. I also include the list of topics
and I comment on them.

Structure of Complexity Classes (Do they keep this topic for traditions sake?)

Reducibilities and Completeness.

Proof Complexity.

Interactive and Probabilistic Proof Systems.

Inapproximability. (I'm surprised this wasn't on the 1997 list.)

Complexity in other Concrete Computational Models. (Other than what?)

Kolmogorov complexity.

Quantum Complexity. (Not sure when it first entered the list, though it was on the 2002 CFP.)

Circuits Complexity.

Communication Complexity.

Complexity and Logic. (Too general.)

Pseudorandomness and derandomization. (How does this differ from Computational Randomness?)

Average case complexity. (I'm surprised it was not on the 1997 list.)

Complexity and Learning. (What is this still doing on the list?)

Cryptographic complexity.

NOTES:

The only topics on all three lists:
Reducibilities, Kolmogorov Complexity,
Cryptographic complexity. Maybe randomness.
Depending on how you count `Logic and Complexity'
maybe finite model theory.

I was surprised there was NOTHING on concrete models
of complexity in 1986. Furst-Saxe-Sipser was already
known (1981 FOCS, 1984 MST) so I would think Circuits
would be of interest. Realize that FSS was first presented
as an attempt
to get an oracle that separates PH from PSPACE
(which later succeeded- Yao and Hastad).
You can feel the paradigm shifting and circuits becoming
important unto themselves as opposed to servicing
recursion-theoretic complexity.

Perhaps I shouldn't be surprised- the list of topics may lag
behind the reality. It takes a few years to catch up.

The number-of-topics has grown from 10 to 12 to 15.
At this rate...

The change to the topics seems to have come WITHOUT an old guard
resisting the change. Why was this? TCS is young enough that people
could change fields? TCS is young enough to not have an old guard?

6 comments:

I always thought that "structure of complexity classes" referred to things like Ladner's theorem or the Berman-Hartmanis isomorphism conjecture, i.e., properties of a complexity class beyond its mere existence as an arbitrary set of strings.

To answer one of Bill's questions, there have been at least a half-dozen papers on complexity and learning at CCC in the past decade.

I searched for the string "learn" in the CCC proceedings tables of contents going back to 2001. There were papers whose titles include the term "learning" or "learnability" in 2001, 2002, 2005, 2006, 2008, 2009 and 2010, including Oded Regev's invited talk and survey paper on "The Learning with Errors Problem" in 2010.

I imagine that looking beyond just paper titles would turn up additional CCC papers that are related to learning.

It is interesting that the terms "sampling", "validation", and "verification" appear in none of the lists ... and yet in practice, these three are among the most ubiquitous, most difficult, and most interrelated computational challenges that we face.

You showed the 2008 list in column-major order. In writing out the revisions of the 2007 list from the PC, I assumed that it would be read in row-major order. In that case, "other concrete computational models" would be read after "circuit complexity" and "communication complexity". (BTW: This did not represent order of importance at all.)

"Computational Randomoness" and "Kolmogorov complexity" seemed to have too much overlap so the PC chose to make the split clearer.

Yes. It was tradition to keep the first topic and the sense in Timothy Chow's comment seems correct: As I understand it, it refers to how the entire web of complexity classes gives a structure within which we can classify computational problems. This includes containments, collapses, reducibility, etc and may be expressed as in the complexity zoo diagram.

When "Structures" started in 1986, the "concrete" side of complexity was very well represented in STOC/FOCS (Barrington's simulation of NC^1 by constant width BPs and Hastad's parity lower bound were among the highlights of that year's STOC) but other aspects of complexity were not and those were emphasized in the call. It was clearly a mistake and some of the papers at the first Structures were definitely "concrete". (e.g., James Lynch's paper on AC^0 lower bounds for small cliques was at the first one and Kalyanasundaram and Schnitger's original randomized CC lower bounds for disjointness were at the second.)